In the feedforward part of an SI (Spark Ignition) engine Air/Fuel control system, the in-cylinder mass air flow rate should be accurately estimated in order to determine the amount of fuel to be injected. Generally, this evaluation is performed either with a dedicated physical sensor (MAF sensor) or more often through an indirect evaluation.
To meet strict emission regulations, automobile gasoline engines are equipped with a three-way catalytic converter (TWC). A precise control of the air-fuel ratio (A/F) to maintain it as close as possible to the stoichiometric value is necessary to achieve a high efficiency of the TWC converter in the conversion of the toxic exhaust gases (CO, NOx, HC) into less harmful products (CO2, H2O, N2). Typically, in a spark-ignition engine, this control is performed through a so-called lambda sensor. The lambda sensor generates a signal representative of the value of the ratio
  λ  =            Air      /      Fuel              Air      /              Fuel        stoichiometric            from the amount of oxygen detected in the exhaust gas mixture. If λ<1 the mixture is rich of fuel, while if λ>1 the mixture is lean of fuel.
To keep the air/fuel ratio (AFR) as close as possible to unity, the lambda sensor is introduced in the conduit or stream of exhaust gases for monitoring the amount of oxygen present in the exhaust gas mixture. The signal generated by the lambda sensor is input to the controller of the engine that adjusts the injection times and thus the fuel injected during each cycle for reaching the condition λ=1.
Traditional Air/Fuel control systems include a feed-forward part, in which the amount of fuel to be injected is calculated on the basis of the in-cylinder mass air flow, and a feedback part that uses the signal of the oxygen sensor (lambda sensor) in the exhaust gas stream, to ensure that the Air/Fuel remain as close as possible to the stoichiometric value (e.g. Heywood, J.B., -“Internal combustion engine fundamentals”-McGraw-Hill Book Co., 1988.).
FIG. 1 shows a block diagram of a traditional Air/Fuel control system. Generally, the feedback part of the Air/Fuel control system is fully active only in steady-state conditions. Moreover, the lambda sensor signal is made available only after this sensor has reached a certain operating temperature. In transients and under cold start conditions, the feedback control is disabled, thus the feedforward part of Air/Fuel control becomes particularly important.
As mentioned above, air flow estimation is often the basis for calculating the amount of injected fuel in the feedforward part of Air/Fuel control system.                A conventional technique for estimating a cylinder intake air flow in a SI (Spark Ignition) engine involves the so-called “speed-density” equation:        
            m      .        ap    =            η      ⁡              (                              p            m                    ,          N                )              ·                            V          d                ·        N        ·                  p          a                            120        ·        R        ·                  T          m                    where {dot over (m)}ap is the inlet mass air flow rate, Vd is the engine displacement and N is the engine speed; Tm and pm are the average manifold temperature and pressure and η is the volumetric efficiency of the engine. This is a nonlinear function of engine speed (N) and manifold pressure (pm), that may be experimentally mapped in correspondence with different engine working points.
A standard method is to map the volumetric efficiency and compensate it for density variations in the intake manifold.
One of the drawbacks in using the “speed-density” equation for the in-cylinder air flow estimation is the uncertainty in the volumetric efficiency. Generally, the volumetric efficiency is calculated in the calibration phase with the engine under steady state conditions. However variations in the volumetric efficiency due, for example, to engine aging and wear, combustion chamber deposit buildup etc., may introduce errors in the air flow estimation.
The low-pass characteristic of commercial sensors (Manifold Absolute Pressure or MAP sensors) used for the determination of the manifold pressure pm, introduces a delay that, during fast transients, causes significant errors in the air flow determination.
This problem is not solved by using a faster sensor because in this case the sensor detects also pressure fluctuations due to the valve and piston motion (e.g. Barbarisi, et al., “An Extended kalman Observer for the In-Cylinder Air Mass Flow Estimation”, MECA02 International Workshop on Diagnostics in Automotive Engines and Vehicles, 2001).
In engines equipped with an EGR (Exhaust Gas Recirculation) valve, the MAP (Manifold Absolute Pressure) sensor cannot distinguish between fresh air (of known oxygen content) and inert exhaust gas in the intake manifold. Therefore, in this case the speed-density equation (1) cannot be used and the air charge estimation algorithm should provide a method for separating the contribution of recycled exhaust gas to the total pressure in the intake manifold (e.g. Jankovic, M., Magner, S.W., “Air Charge Estimation and Prediction in Spark Ignition Internal Combustion Engines”, Proceedings of the American Conference, San Diego, California, June 1999).
An alternative method for the air charge determination is to use a dedicated Mass Air Flow (MAF) physical sensor, located upstream the throttle, that directly measures the inlet mass air flow. The main advantages of a direct air flow measurement are: automatic compensation for engine aging and for all other factors that modify engine volumetric efficiency; improved idling stability; and lack of sensibility of the system to EGR (Exhaust Gas Recirculation) since only the fresh air flow is measured.
Anyway, air flow measurement by means of a MAF sensor (which is generally a hot wire anemometer) accurately estimates the mass flow in the cylinder only in steady state because during transients the intake manifold filling/empting dynamics play a significant role (e.g. Grizzle, J.W., Cookyand, J.A., and Milam, W.P., “Improved Cylinder Air Charge Estimation for Transient Air Fuel Ratio Control”, Proceedings of American Control Conference, 1994; and Stotsky, I., Kolmanovsky, A., “Application of input estimation and control in automotive engines” Control Engineering Practice 10, pp. 1371-1383, 2002).
Moreover, for commercial automotive applications, the fact that a MAF sensor has a relatively high cost compared to the cost of MAP (Manifold Absolute Pressure) sensor used with the “speed density” evaluation approach, should be taken into account.